Final answer:
Adding a constant K to each data point in a given set increases the mean by K but leaves the standard deviation unchanged, since it does not affect the spread of the numbers.
Step-by-step explanation:
When the same constant K is added to each value in a data set, the mean (denoted by μ) of the data set increases by K. This is because the mean is the average of all data points, so by increasing each data point by K, you increase the sum of the data points by K times the number of data points. When you divide this new sum by the number of data points to get the mean, the result is the original mean plus K. The standard deviation (denoted by σ), on the other hand, does not change when you add a constant K to each data value. This is because standard deviation measures the spread of a set of numbers and is calculated using the deviations of the numbers from their mean. Adding K to each number shifts each number by K, but does not affect the distance between the numbers.